Lower Bounds on the Bottleneck Complexity of Secure Multiparty Computation

Secure multiparty computation (MPC) is a cryptographic primitive which enables multiple parties to jointly compute a function without revealing any extra information on their private inputs. Bottleneck complexity is an efficiency measure that captures the load-balancing aspect of MPC protocols, defined as the maximum amount of communication required by any party. In this work, we study the problem of establishing lower bounds on the bottleneck complexity of MPC protocols. While the previously known techniques for lower bounding total communication complexity can also be applied to bottleneck complexity, they do not provide nontrivial bounds in the correlated randomness model, which is commonly assumed by existing protocols achieving low bottleneck complexity, or they are applied only to functions of limited practical interest. We propose several novel techniques for lower bounding the bottleneck complexity of MPC protocols. Our methods derive nontrivial lower bounds even in the correlated randomness model and apply to practically relevant functions including the sum function and threshold functions. Furthermore, our lower bounds demonstrate the optimality of some existing MPC protocols in terms of bottleneck complexity or the amount of correlated randomness.